the infinite
“Monads, Situation and Infinite Explanation,” with Filippo Costantini, British Journal for the History of Philosophy, April, 2025: [Monads situation and infinite explanation.pdf] —also at https://doi.org/10.1080/09608788.2025.2478974.
“Monads and Points, Contiguity and Transcreation: on the Development of Leibniz’s Metaphysics of the Continuum,” Archiv für Geschichte der Philosophie, August 2025, [Monads and Points.pdf]
“On the Unviability of Interpreting Leibniz’s Infinitesimals through Nonstandard Analysis”, with David Rabouin, Historia Mathematica, March 2024, vol. 66, 26-42; [Unviability.pdf]
“Leibniz and the Three Degrees of Infinity”, pp. 25–46, in Leibniz Review, 32, 2022; with a reply from Ohad Nachtomy [Three.Degrees.LR.2022.pdf].
A Question of Fundamental Methodology: Reply to Mikhail Katz”, co-authored with Tom Archibald, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper Lützen, Marco Panza, David Rabouin, and Gert Schubring, pp. 360–363 in The Mathematical Intelligencer, 44, 4, Winter 2022. [A Question of Fundamental Methodology.pdf]
“Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of Differential Calculus” (co-authored with David Rabouin), Archive for History of Exact Sciences, 2020, 74, 5, 401 – 443; DOI: 10.1007/s00407-020-00249-w.[Rabouin-Arthur-infinitesimals.pdf]
“Leibniz in Cantor’s Paradise: A Dialogue on the Actual Infinite”, ch. 3, pp. 71-109 in Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, Epistemology, ed. Vincenzo De Risi, Cham, Switzerland: Springer, 2019. [Leibniz in Cantor’s Paradise.pdf]
“Leibniz’s Syncategorematic Actual Infinite”, pp. 155-179 in Infinity in Early Modern Philosophy, eds. Ohad Nachtomy and Reed Winegar, Springer Verlag, 2018. [L’s.Sync.Actu.Inf.pdf].
“The Labyrinth of the Continuum”, in Maria Rosa Antognazza (ed.), Oxford Handbook of Leibniz; published online at (www.oxfordhandbooks.com), Oxford: Oxford University Press, December 2013. [The_Labyrinth_of_the_Continuum.pdf]
“Leibniz’s Syncategorematic Infinitesimals, Smooth Infinitesimal Analysis, and Second Order Differentials”, Archive for History of Exact Sciences, April 2013. [LSI.pdf]
“Leibniz’s Actual Infinite in Relation to his Analysis of Matter”, 137-156 (chapter 7) in G. W. Leibniz on the interrelations between mathematics and philosophy, (Springer: Archimedes Series), ed. Norma Goethe, Philip Beeley and David Rabouin, 2012. [Lairam.pdf]
“Presupposition, Aggregation, and Leibniz’s Argument for a Plurality of Substances”, Leibniz Review, 21, 91-116, 2011. [PresuppAggLAPS.pdf]
“Actual Infinitesimals in Leibniz’s Early Thought”, in The Philosophy of the Young Leibniz, Studia Leibnitiana Sonderhefte 35, ed. Mark Kulstad, Mogens Laerke and David Snyder, 2009, pp. 11-28. [Actual_Infinitesimals.pdf]
“Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals,” pp. 7-30 in Infinitesimal Differences: Controversies between Leibniz and his Contemporaries, ed. Ursula Goldenbaum and Douglas Jesseph, Berlin and New York: De Gruyter, 2008. [Leery.Bedfellows2008.pdf]
Also available are these preprints:
“Leibniz’s Archimedean infinitesimals,” Proceedings of the Canadian Society for History and Phil. of Mathematics, 21, 1-10, 2008. [preprint]
“Leibniz and Cantor on the Actual Infinite,” pp. 41-46 in Nihil sine ratione , Vol. 1, ed. Hans Poser, Berlin: Gottfried-Willhelm-Leibniz-Gesellschaft, 2001. [preprint]
“The remarkable fecundity of Leibniz’s work on infinite series”: a review article on 2 Akademie volumes of Leibniz’s writings, VII, 3: 1672-76: Differenzen, Folen Reihen, and III, 5: Mathematischer, naturwissenschaftlicher und technischer Briefwechsel, 2012. [preprint]
September 13, 2026